Doppler spectral moments

From AMS Glossary
(Difference between revisions)
Jump to: navigation, search
(Created page with " {{TermHeader}} {{TermSearch}} <div class="termentry"> <div class="term"> == Doppler spectral moments == </div> <div class="definition"><div class="short_definition">St...")
 
 
Line 9: Line 9:
 
   </div>
 
   </div>
  
<div class="definition"><div class="short_definition">Statistical moments of Doppler frequency or [[Doppler velocity]], regarding  these quantities as continuously distributed [[random]] variables with a [[probability density  function]] equal to the normalized [[Doppler spectrum]].</div><br/> <div class="paragraph">If ''S''(''f'') denotes the Doppler spectrum as a function of Doppler frequency ''f,'' the ''n''th [[moment]]  is defined by  <div class="display-formula"><blockquote>[[File:ams2001glos-De39.gif|link=|center|ams2001glos-De39]]</blockquote></div> where the denominator normalizes the Doppler spectrum to unit area. The ''n''th moment in terms  of Doppler velocity is related to that in terms of [[frequency]] by  <div class="display-formula"><blockquote>[[File:ams2001glos-De40.gif|link=|center|ams2001glos-De40]]</blockquote></div> where &lambda; is the radar [[wavelength]]. The first [[moment]] of [[velocity]] is called the [[mean Doppler  velocity]] and the second [[central moment]] is called the Doppler velocity [[variance]]. The [[Doppler  spread]] usually denotes the square root of the Doppler velocity variance. <br/>''See'' [[Doppler frequency  shift]].</div><br/> </div>
+
<div class="definition"><div class="short_definition">Statistical moments of Doppler frequency or [[Doppler velocity]], regarding  these quantities as continuously distributed [[random]] variables with a [[probability density function|probability density  function]] equal to the normalized [[Doppler spectrum]].</div><br/> <div class="paragraph">If ''S''(''f'') denotes the Doppler spectrum as a function of Doppler frequency ''f,'' the ''n''th [[moment]]  is defined by  <div class="display-formula"><blockquote>[[File:ams2001glos-De39.gif|link=|center|ams2001glos-De39]]</blockquote></div> where the denominator normalizes the Doppler spectrum to unit area. The ''n''th moment in terms  of Doppler velocity is related to that in terms of [[frequency]] by  <div class="display-formula"><blockquote>[[File:ams2001glos-De40.gif|link=|center|ams2001glos-De40]]</blockquote></div> where &lambda; is the radar [[wavelength]]. The first [[moment]] of [[velocity]] is called the [[mean Doppler velocity|mean Doppler  velocity]] and the second [[central moment]] is called the Doppler velocity [[variance]]. The [[Doppler spread|Doppler  spread]] usually denotes the square root of the Doppler velocity variance. <br/>''See'' [[Doppler frequency shift|Doppler frequency  shift]].</div><br/> </div>
 
</div>
 
</div>
  

Latest revision as of 17:49, 25 April 2012


[edit] Doppler spectral moments

Statistical moments of Doppler frequency or Doppler velocity, regarding these quantities as continuously distributed random variables with a probability density function equal to the normalized Doppler spectrum.

If S(f) denotes the Doppler spectrum as a function of Doppler frequency f, the nth moment is defined by
ams2001glos-De39
where the denominator normalizes the Doppler spectrum to unit area. The nth moment in terms of Doppler velocity is related to that in terms of frequency by
ams2001glos-De40
where λ is the radar wavelength. The first moment of velocity is called the mean Doppler velocity and the second central moment is called the Doppler velocity variance. The Doppler spread usually denotes the square root of the Doppler velocity variance.
See Doppler frequency shift.

Personal tools
Namespaces
Variants